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Related Concept Videos

Time and frequency -Domain Interpretation of Phase-lead Control01:24

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Phase-lead controllers are commonly used in various control systems to enhance response speed and stability. Adjusting the brightness on a television screen offers a practical example of phase-lead control. When contrast is enhanced, a phase-lead controller is employed. Mathematically, phase-lead control is identified when the first parameter is smaller than the second.
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Time and frequency -Domain Interpretation of Phase-lag Control01:21

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Phase-lag controllers are widely used in control systems to improve stability and reduce steady-state errors. A dimmer switch controlling the brightness of a light bulb serves as a practical example of phase-lag control, gradually adjusting the bulb's brightness. Mathematically, phase-lag control or low-pass filtering is represented when the factor 'a' is less than 1.
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Phase-lead and Phase-lag Controllers01:22

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Understanding the working function of different types of controllers can be illustrated with practical analogies, such as adjusting a stereo's volume equalizer. Cranking up the bass involves a phase-lead controller, which functions as a high-pass filter, while increasing the treble uses a phase-lag controller, which acts as a low-pass filter. PD controllers, similar to high-pass filters, enhance the system's response to high-frequency components. PI controllers, akin to low-pass...
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Phasor Arithmetics01:13

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Phasors and their corresponding sinusoids are interrelated, offering unique insights into the behavior of alternating current (AC) circuits. One way to understand this relationship is through the operations of differentiation and integration in both the time and phasor domains.
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Gain and phase shift are properties of linear circuits that describe the effect a circuit has on a sinusoidal input voltage or current. The circuit's behavior that contains reactive elements will depend on the frequency of the input sinusoid. As a result, it is observed that the gain and phase shift will all be frequency functions.
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Phasors are a powerful mathematical tool used to analyze alternating current (AC) circuits. They provide a complex number representation of sinusoids, with the magnitude of the phasor equating to the amplitude of the sinusoid and the angle of the phasor representing the phase measured from the positive x-axis.
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Gain-compensation Methodology for a Sinusoidal Scan of a Galvanometer Mirror in Proportional-Integral-Differential Control Using Pre-emphasis Techniques
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Phase estimation using phase gradients obtained through Hilbert transform.

P A Ameen Yasir, J Solomon Ivan

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    |November 10, 2016
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    Summary
    This summary is machine-generated.

    A new algorithm accurately unwraps phase from interferograms with distorted fringes. It uses Hilbert transforms and least squares for precise phase gradient estimation, validated with simulated and real-world data.

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    Area of Science:

    • * Optical interferometry
    • * Signal processing
    • * Phase retrieval

    Background:

    • * Interferograms often contain perturbed fringes, complicating phase extraction.
    • * Accurate phase unwrapping is crucial for quantitative analysis in various optical techniques.

    Purpose of the Study:

    • * To develop and validate an algorithm for unwrapping phase from interferograms with perturbed straight line fringes.
    • * To improve the accuracy and robustness of phase retrieval in optical metrology.

    Main Methods:

    • * Phase gradients extracted using the Hilbert transform.
    • * Phase estimation from gradients via the method of least squares for Hudgin geometry.
    • * Analytical matrix inversion exploiting Hudgin matrix symmetries.

    Main Results:

    • * Successful phase unwrapping demonstrated on numerically generated interferograms.
    • * Algorithm validated on experimental data from a Mach-Zehnder interferometer.
    • * Consistent performance observed with random and atmospheric turbulence-like phase perturbations.

    Conclusions:

    • * The proposed algorithm effectively extracts unwrapped phase from complex interferograms.
    • * Analytical simplification of the least squares method enhances computational efficiency.
    • * The method shows promise for applications requiring precise phase measurements in disturbed optical systems.